Browsing by Author "Haque, Shajid"

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    A study of circuit Complexity for Coherent States
    (2022) Tladi, Mpho; Haque, Shajid; Murugan, Jeffrey; Weltman, Amanda
    Computational complexity is a popular quantity in quantum information theory. It has made huge strides in recent years in the study of black hole dynamics. A brief definition of complexity is the measure of how difficult it is to implement a task. For a quantum system, complexity evaluates the difficulty of preparing a quantum state from a given reference state by unitary transformations. However, in the dual gravity theory complexity has a geometric meaning. In some black hole context, Leonard Susskind and collaborators proposed two holographic conjectures. The Complexity=Volume (CV) states that complexity of the boundary field theory is dual to the volume of a co dimension one maximal surface that extends to the boundary of the Ads space. Complexity=Action (CA) posits that complexity of the boundary is the same as the action evaluated as an action on patch in the bulk defined as the Wheeler De Witt patch. In recent years, these two conjectures have initiated an extensive study of complexity. This thesis is also motivated by these conjectures and will investigate complexity in the field theory side of the story. Specifically, we will explore the complexity for coherent states. We will start with a review of different methods of computing complexity. Finally, we then investigate the complexity for coherent states by using the methods of circuit complexity and operator complexity
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    A study on complexity
    (2023) Rapotu, Dimakatso; Haque, Shajid; Murugan Jeffrey
    This thesis explores quantum complexity for various quantum systems. Quantum complexity is a well defined quantity in quantum information theory that measures the difficulty of constructing a quantum state from a given reference state and so far, various methods within high energy physics communities have been proposed for computing complexity. In this thesis, we will first review the computations of the different methods used for computing complexity, such as the circuit complexity that uses the wave function, Fubini-Study complexity, and finally the recently proposed Krylov complexity for closed quantum systems. We then extend our investigation and review the complexity for some open quantum systems that have already been explored in literature and finally, we will make some progress by also extending the investigation towards computing the complexity of a new open quantum system, namely the non-gaussian random matrix model.
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    Carroll physics in general relativity: understanding the Carroll limit of the singularity theorem
    (2025) Thapo, Thato; Haque, Shajid; Underwood, Bret
    The Carroll limit of general relativity is an ultra-relativistic limit that is obtained by taking the speed of light (c) to zero. This is in contrast to the Galilean limit, where you can resolve it by taking the c → ∞ limit. This limit was formulated in the study of the Carroll group as an ultra-relativistic limit of the Poincaré group, as such, one can exploit the various Carroll symmetries that arise. In this thesis, we study the Carroll limit of general relativity and its applications to Cosmology and the Singularity Theorem. We begin by reviewing the representation theory of the Carroll group and its applications to non-relativistic physics. We then study the Carroll scalar field and its properties in the Carroll limit, as well as how the Friedmann equations reduce in the small c expansion in comparison to the evolution of the scalar field in our Standard Cosmology. We then study how fluids evolve in the Carroll regime, which gives us insight into the early universe and its dynamics. This study allows us to explore how non-relativistic matter, as well as the cosmological constant, would evolve in the Carroll limit. To understand radiation in the Carroll limit, we take a purely Classical route and study Maxwell's Theory of electromagnetism in a curved background. That then allows us to study the singularity theorem and how singularities are affected by taking this limit, which prompts us to look into a relatively recent theorem known as the BGV theorem, which looks at singularities from the perspective of geodesic incompleteness in contrast to the Hawking and Penrose ideas on the singularity theorem.